How would an AI work out this question?
I don't think that the "try all the numbers" approach is very representative, because I'm not sure whether or not the agent that uses that approach can be considered by any means AI.

There is no "intelligence" in just checking numbers to try to prove the statement. An agent that is considered to be intelligent should apply a more intelligent approach.

This becomes more evident because the question aims at exploiting the lack of scalability of the agent's strategy. If the question was "Prove that no number exists which is one more than 5", then the agent would have no trouble in finding the correct answer.